Related papers: Untangling Surface Codes: Bridging Braids and Latt…
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
Modelling the vascular transport and adhesion of man-made particles is crucial for optimizing their efficacy in the detection and treatment of diseases. Here, a Lattice Boltzmann and Immersed Boundary methods are combined together for…
We propose a novel, distillation-free scheme for the fault-tolerant implementation of non-Clifford gates at the logical level, thereby completing the universal gate set. Our approach exploits generalized lattice surgery to integrate two…
Hook errors are a major challenge in implementing logical operations with the surface code, because they can reduce the fault distance below the code distance. This motivates syndrome-extraction circuits that suppress hook-error effects for…
In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such…
Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical…
A lattice version of quantum nonlinear Schrodinger (NLS) equation is considered, which has significantly simple form and fullfils most of the criteria desirable for such lattice variants of field models. Unlike most of the known lattice…
The maximum likelihood (ML) decoder in the two-dimensional surface code with generic unitary errors is governed by a statistical mechanics model with complex weights, which can be simulated via (1+1)D transfer matrix contraction.…
Bridge multisections are combinatorial descriptions of surface links in 4-space using tuples of trivial tangles. They were introduced by Islambouli, Karimi, Lambert-Cole, and Meier to study curves in rational surfaces. In this paper, we…
We introduce a new approach to the numerical simulation of Scanning Transmission Electron Microscopy images. The Lattice Multislice Algorithm (LMA) takes advantage of the fact that electron waves passing through the specimen have limited…
Fluid simulations, especially at high Reynolds numbers, are computationally expensive on classical computers, making them promising application targets for quantum computing. Recent studies have combined the lattice Boltzmann method (LBM)…
Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling…
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…
In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with…
Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard…
We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs,…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging…